K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will “invent” examples that demonstrate the Commutative Property of Addition (i.e., that “In addition, no matter in which order addends are placed, the sum will always be the same.”).

Teacher planning

Time required for lesson

1 hour


For each student (or group of two students):

  • Two sets of five “counting bears” (each set a different color).
  • Two sets of numerals 0-5 (each set a different color to match bears). Die-cut tagboard numerals would be ideal.
  • One set of black die-cut numerals (0-10) for sums.
  • A Work Mat (of your own design) containing an “addition sign” an “equals sign” and an “answer circle.” Students will physically move bear addends to the “answer circle.”

Technology resources

Computer, printer, and Internet connection to download and print “Sample Test.”


Students must be able to add single digits to 10.



Teacher explains Commutative Property of Addition and demonstrates to students by the various means below:

  1. Using Work Mat, present set of 2 red bears + set of 1 yellow bear (2+1=3). Reverse order of addends to show that the sum will always be the same (1+2=3). Combine bears for sums in the “answer circle.” Repeat with several examples of increasing difficulty.
  2. Pair colored die-cut numerals with bear sets above and repeat exercises above. Combine bear sets and use black numerals for sums in the “answer circle.”
  3. Use colored die-cut numerals in isolation and repeat exercises above. Use black numerals for sums in the “answer circle.”

Student Activities

  1. Distribute bear sets to each student (or group of two students). Repeat #1 above and ask each student (or group) to duplicate the examples you demonstrate on their Work Mats. After circulating to check for understanding, invite students to “invent” other combinations to show the commutative property of addition.
  2. Distribute die-cut numeral sets. Ask students to pair colored numerals with bear sets on their Work Mats and black numerals in the “answer circle” to demonstrate the commutative property of addition.
  3. Ask students to use colored die-cut numerals on their Work Mats in isolation and black numerals in the “answer circle” to demonstrate the Commutative Property of Addition.
  4. Probe class to determine understanding by asking them to verbally describe the Commutative Property of Addition. Get approximately five (correct) responses.
  5. Probe class to determine how they will use what they have learned. Ask for examples. Get approximately five (correct) responses.


  1. Review concept and operations above.
  2. Tell students they will now be tested on their understanding.


Distribute test consisting of single digit addition problems to ten (see sample attachment).

  • First, ask your students to solve each of the problems given.
  • Second, ask your students to re-write the original problems in “reverse order” in the space next to the original problems and solve.
  • Third, ask your students to give a written explanation about what they have learned.
  • Finally, ask your students to give a written explanation about how they will use what they have learned.

Supplemental information


Colored chips, bottle caps, etc. can be substituted for “counting bears.”

3X5 cards with colored numerals can be substituted for die-cut numerals.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 1

        • Operations & Algebraic Thinking
          • 1.OAT.3 Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 +...
        • Kindergarten

          • K.OAT.1Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
          • K.OAT.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

North Carolina curriculum alignment

Mathematics (2004)

Grade 1

  • Goal 1: Number and Operations - The learner will read, write, and model whole numbers through 99 and compute with whole numbers.
    • Objective 1.04: Create, model, and solve problems that use addition, subtraction, and fair shares (between two or three).